Krovak projection EPSG 5514: Correct data transfer between R and ArcGIS?

Question

I have a problem which many ArcGIS, QGIS and R users from Czech Republic and Slovakia may encounter. In ArcGIS, I am working EPSG: 5514, Projected Coordinate System, defined as:

S-JTSK_Krovak_East_North
WKID: 5514 Authority: EPSG

Projection: Krovak
False_Easting: 0.0
False_Northing: 0.0
Pseudo_Standard_Parallel_1: 78.5
Scale_Factor: 0.9999
Azimuth: 30.28813975277778
Longitude_Of_Center: 24.83333333333333
Latitude_Of_Center: 49.5
X_Scale: -1.0
Y_Scale: 1.0
XY_Plane_Rotation: 90.0
Linear Unit: Meter (1.0)

Geographic Coordinate System: GCS_S_JTSK
Angular Unit: Degree (0.0174532925199433)
Prime Meridian: Greenwich (0.0)
Datum: D_S_JTSK
  Spheroid: Bessel_1841
    Semimajor Axis: 6377397.155
    Semiminor Axis: 6356078.962818189
    Inverse Flattening: 299.1528128

When I load my file in R, my proj4string(data_in_5514) shows:

 "+proj=krovak +lat_0=49.5 +lon_0=24.83333333333333 +k=0.9999 +x_0=0 +y_0=0 +ellps=bessel +units=m +no_defs"

I've got the same information when I export my files from R using writeRaster() function from raster package. However, when I want to open my data modified in R again in ArcGIS, my ArcGIS crashes, and if I am lucky, I've got a warning message :

Warning, inconsistent extent!

which means (http://support.esri.com/em/knowledgebase/techarticles/detail/37732):

This error message is returned if the data has an incorrect projection definition.

Specifically, the data is in a projected coordinate system with units of feet, meters or other linear units, but the projection has been defined with a Geographic Coordinate System (GCS) that has units in decimal degrees.

Thus, obviously the projection of my data has changed, but when and how ???

How can I correctly transfer data between R and ArcGIS using Krovak EPSG 5514? I've also found, that this one PCS is also listed as EPSG: 102067 under ArcGIS, however, R doesn't recognize this code.

EDIT :

sample data: http://ulozto.sk/xNHrBv2D/r3-zip

as an output I was using several formats. I was able to opet Gtiff once, .img neidther one time, .grd seems not to be directly recognized by ArcGIS.

export data:

writeRaster(aaa, filename="r3.img", format="HFA", overwrite=TRUE)
# export data
writeRaster(aaa, filename="r3.tif", format="GTiff", overwrite=TRUE)
# export data
writeRaster(aaa, filename="r3", overwrite=TRUE)  # creates a .grd

Answer 1

I suggest to remove projection information in R output raster and open it in ArcGIS. If successful, define projection from within latter.

I applied this trick with vectors coming from MapInfo to ESRI products. Slight difference in projection naming by these two packages had devastating result with points being 200 m away from their true position. Good example of it is projection called GD_1949_New_Zealand_Map_Grid in ArcGIS.